# Month: July 2020

## Normal Approximation … or Not?

(A new question of the week) A recent question (from May) about approximating the binomial distribution with the normal distribution led to some (accidental and otherwise) insights about the method. I have to solve this problem: A manufacturing company uses an acceptance scheme on items from a production line before they are shipped. The plan …

## Multiplying Vectors II: The Vector Product

Last time, we looked at the scalar, or dot, product of vectors, focusing on proving the equivalence of two ways to define it. This time, we’ll look at the vector, or cross, product in the same way. The distinction between dot and cross product reflects the symbol used, u · v vs. u × v, …

## Proving Proportions, Problematic Products

(A new question of the week) A recent question provided an opportunity to examine some ideas about ratios, and also ways to tame a potentially huge product. Proving one proportion from another Here is the question, received from Sithum in late April: Hi Dr. Math! There are some problems that involve a given ‘equation with …

## Multiplying Vectors I: The Scalar Product

Having covered the basics of defining and adding vectors, multiplying by scalars and finding unit vectors, it’s time to look at multiplying vectors together. What makes this entirely unlike working with numbers is that there are two ways (in fact, more than two!) to multiply two vectors. We’ll look at one of those today, the …

## Vector Basics: Describing Directions

We’re looking at the concept of vectors at an introductory level. Last week we looked at how they are defined in this context (as quantities with magnitude and direction), and how they are added (which is really part of the definition). Our collection of answers from Ask Dr. Math this time focuses on the ideas …

## A Rate Problem: Two Speeds, Two Ways

(A new question of the week) A question we got at the end of March asked about a standard kind of algebra word problem that can be solved in a couple very different ways. It illustrates several choices that can be made (both about the meaning of the problem and how to solve it), as …